Recently it has been shown that N = 4 super Yang-Mills theory is integrable in the planar
limit. Past arguments suggest the integrability is only present in the planar limit. However,
this conclusion was shown to be incorrect. Two speci c classes of operators were studied in the O(N) sector. The rst were labelled by Young diagrams having two long columns.
The second were labelled by Young diagrams having two long rows. This result was then
generalized to p long rows or columns with p xed to be O(1) as N ! 1. For this case, the
non-planar limit was found to be integrable. In this dissertation, we extend this work by
considering p to be O(N). We have calculated the dilation operator for the case with two
impurities
